Direct Integration Research Articles

Performance of GRKM-method for solving classes of ordinary and partial differential equations of sixth-orders

Abstract A general quasilinear sixth-order ordinary differential equation (ODE) is an important class of ODEs. The primary objective of this study is to establish a numerical method for solving a general class of quasilinear sixth-order partial differential equations (PDEs) and ODEs. However, the Runge–Kutta method (RKM) approach for solving special classes of ODEs has been generalized as an effort to solve the general class of ODEs. Nonlinear algebraic order condition (OCs) equations have been obtained up to the tenth order using the Taylor-series expansion methodology which is used to derive the novel generalized Runge–Kutta method (GRKM). In this study, a GRKM integrator has been derived for solving a general class of quasilinear sixth-order ODEs and then this method is modified subsequently to solve a class of PDEs. Accordingly, the proposed GRKM is modified to solve a quasilinear sixth-order PDE by converting it to a system of sixth-ODEs using the method of lines. Nine problems have been implemented to prove the efficiency and accuracy of the proposed method. Simulation results of these problems showed that the proposed numerical GRKM is an accurate and efficient method. In contrast, by comparing the proposed GRKM numerical approach with the classical RK method, the numerical results demonstrate that the direct integrator outperforms the indirect classical RK method in terms of algorithm complexity and function evaluations, proving that the numerical GRKM is efficient.

CLASS-OneLoop: accurate and unbiased inference from spectroscopic galaxy surveys

The power spectrum is the most commonly applied summary statistics to extract cosmological information from the observed three-dimensional distribution of galaxies in spectroscopic surveys. We present CLASS-OneLoop, a new numerical tool, fully integrated into the Boltzmann code CLASS, enabling the calculation of the one-loop power spectrum of biased tracers in spectroscopic surveys. Built upon the Eulerian moment expansion framework for redshift-space distortions, the implemented model incorporates a complete set of nonlinear biases, counterterms, and stochastic contributions, and includes the infrared resummation and the Alcock-Paczynski effect. The code features an evaluation of the loops by either direct numerical integration or Fast Fourier Transform, and employs a fast-slow parameter decomposition, which is essential for accelerating MCMC runs. After presenting performance and validation tests, as an illustration of the capabilities of the code, we apply it to fit the measured redshift-space halo power spectrum wedges on a ΛCDM subset of the AbacusSummit simulation suite and considering scales up to kmax = 0.3 h/Mpc. We find that the one-loop model adeptly recovers the fiducial cosmology of the simulation, while a simplified model commonly used in the literature for sensitivity forecasts yields significantly biased results. Furthermore, we conduct Monte Carlo Markov Chain (MCMC) forecasts for a DESI-like survey, considering a model with a dynamical dark energy component. Our results demonstrate the ability to independently constrain cosmological and nuisance parameters, even in the presence of a large parameter space with twenty-nine variables.

Analytical Analysis of the Bladeless Rotor Turbine Design for Enhanced Performance

The growing desire for clean and efficient energy solutions has fueled considerable advances in turbine technology. This study proposed a conceptual approach to enhancing the performance of bladeless turbines using an analytical technique, and the analytical solutions bear a resemblance to the experimental setup for a fluid dynamics investigation of a rotor for real-flow effects. The Navier-Stokes equations for fluid flow in cylindrical coordinates were simplified to two-dimensional flow by ignoring axial direction and velocity, and direct integration was used in conjunction with series expansion solutions. The experiment data were used to verify the rotor's fluid dynamics analytical solutions. The model's result was compared to previously calculated solutions of the fluid dynamics of a disc rotor in a bladeless turbine. The disc turbine models were used to predict radial velocity, tangential velocity, pressure gradient, volumetric flow rate, rotor torque, shear stress on the inner and outer disc walls, and rotor efficiency. The model was validated using experimental data with an efficiency of 23.9%, the theoretical solution model was 34%, and the analytical efficiency was 24.3%. The efficiency comparison of the analytical solutions model to the theoretical solutions model revealed a substantial difference, however, the correlation between computed theoretical and analytical results is significant. Previous studies used computed solutions for models, but current analytical solutions outperformed them. The model's output will be valuable to engineers building the disc turbine. It demonstrates a strong link between the analytical and experimental research of the bladeless turbine.

Stress-strain state of building structures taking into account possible local failure of the element

The issue of choosing a structural design and material for supporting structures is an important technical and economic task at the stage of developing a design solution. It depends on a number of factors: consequence class of the structure, reliability of the design solution, savings in basic building materials. The publication provides a classification of design schemes and types of load-bearing structures used in the corresponding solutions. The disadvantages and advantages of using prefabricated and monolithic structures for the installation and subsequent operation of the structural scheme of buildings and structures are considered. Modern design requirements include ensuring the ability of a damaged structure to adapt to new conditions while continuing to function while ensuring the integrity of human life, property and equipment. New conditions mean the consequences of the occurrence of a certain emergency situation, accompanied by weakening or overloading of the load-bearing structures of a structure or soil foundation: a change in the structural design, a combination of new existing loads and a redistribution of internal forces. The publication reflects the results of assessing the redistribution of the stress-strain state of the elements of the “base - foundations - load-bearing structures” system as a result of the implementation of a hypothetical emergency situation with the exclusion of the load-bearing structure from operation. The case of the collapse of one of the vertical load-bearing elements (local failure of the pylon) of an underground floor, which can be used as a dual-use structure, is considered. Calculations for the stability of the structure against progressive collapse were carried out by numerical modeling in the LIRA SAPR-2019 software using a quasi-static calculation and the method of direct integration of dynamics over time. It has been demonstrated that the method of numerical modeling the joint work of a building with a soil base affects the results of a calculation of the progressive collapse of the building frame. The influence of local collapse of a vertical load-bearing element on the redistribution of stresses and strains in the foundation structures of a building section is assessed. The load on the piles under the pylons around the element removed under the local failure scenario is expected to increase by 15...25%.

A transcriptomic atlas of the human brain reveals genetically determined aspects of neuropsychiatric health

Regulation of gene expression is a vital component of neurological homeostasis. Cataloging the consequences of endogenous gene expression on the physical structure and connectivity of the brain offers a means of unifying trait-associated genetic variation with trait-associated neurological features. We perform tissue-specific transcriptome-wide association studies (TWASs) on over 3,400 neuroimaging phenotypes in the UK Biobank (N= 33,224) using our joint-tissue imputation (JTI)-TWAS method. We identify highly significant associations between predicted expression for 7,192 genes and a wide variety of measures of the brain derived from magnetic resonance imaging (MRI). Our approach generates reproducible results in internal and external replication datasets. Genetically determined expression alone is sufficient for high-fidelity reconstruction of brain structure and organization. We demonstrate complementary benefits of cross-tissue and single-tissue analyses toward an integrated neurobiology and provide evidence that gene expression outside the central nervous system provides unique insights into brain health. As an application, we provide evidence suggesting that the genetically regulated expression of schizophrenia risk genes causally affects over 73% of neurological phenotypes that are altered in individuals with schizophrenia (as identified by neuroimaging studies). Imaging features associated with neuropsychiatric traits can provide valuable insights into underlying pathophysiology. By linking neuroimaging-derived phenotypes with expression levels of specific genes, this resource represents a powerful gene prioritization schema that can improve our understanding of brain function, development, and disease. The use of multiple different cortical and subcortical atlases in the resource facilitates direct integration of these data with findings from a diverse range of clinical neuroimaging studies.

Deciphering diffuse scattering with machine learning and the equivariant foundation model: the case of molten FeO

Bridging the gap between diffuse x-ray or neutron scattering measurements and predicted structures derived from atom–atom pair potentials in disordered materials, has been a longstanding challenge in condensed matter physics. This perspective gives a brief overview of the traditional approaches employed over the past several decades. Namely, the use of approximate interatomic pair potentials that relate three-dimensional structural models to the measured structure factor and its’ associated pair distribution function. The use of machine learned interatomic potentials has grown in the past few years, and has been particularly successful in the cases of ionic and oxide systems. Recent advances in large scale sampling, along with a direct integration of scattering measurements into the model development, has provided improved agreement between experiments and large-scale models calculated with quantum mechanical accuracy. However, details of local polyhedral bonding and connectivity in meta-stable disordered systems still require improvement. Here we leverage MACE-MP-0; a newly introduced equivariant foundation model and validate the results against high-quality experimental scattering data for the case of molten iron(II) oxide (FeO). These preliminary results suggest that the emerging foundation model has the potential to surpass the traditional limitations of classical interatomic potentials.

Numerical Solution to Poisson’s Equation for Estimating Electrostatic Properties Resulting from an Axially Symmetric Gaussian Charge Density Distribution: Charge in Free Space

Poisson’s equation frequently emerges in many fields, yet its exact solution is rarely feasible, making the numerical approach notably valuable. This study aims to provide a tutorial-level guide to numerically solving Poisson’s equation, focusing on estimating the electrostatic field and potential resulting from an axially symmetric Gaussian charge distribution. The Finite Difference Method is utilized to discretize the desired spatial domain into a grid of points and approximate the derivatives using finite difference approximations. The resulting system of linear equations is then tackled using the Successive Over-Relaxation technique. Our results suggest that the potential obtained from the direct integration of the distance-weighted charge density is a reasonable choice for Dirichlet boundary conditions. We examine a scenario involving a charge in free space; the numerical electrostatic potential is estimated to be within a tolerable error range compared to the exact solution.

Heat transfer in shear flow over a still nanofluid: A direct integration approach

Heat transfer in a two-layer fluid system, including shear-driven viscous fluid in the upper layer and still nanofluid in the lower layer, is investigated in this work. Following single phase model for nanofluid, three different types of nanofluids are considered. Different from existing literatures on two-layer fluid flow problem, this work introduces the heat transfer of shear-driven viscous fluid over a still nanofluid which makes this investigation new. The main equations which are partial in nature are reduced to a set of coupled nonlinear ordinary differential equation (ODE) by employing suitable similarity transformations. These ODEs together with the coupled interfacial boundary conditions are supplied to MATLAB software to get the solution numerically. Comparing the results obtained in this study with the previous authoritative research results, the accuracy and correctness of the present research methodology are ensured. The results show that the temperature of the upper fluid and the lower fluid are controlled by the thermophysical properties of different types of nanofluids. Also, opposite behavior of temperature distribution for the upper and the lower fluid are observed.

Energy geo-structures: A review of their integration with other sources and its limitations

Ground Source Heat Pumps, in the framework of Shallow Geothermal Energy Systems, outperform conventional Heating Ventilation and Air Conditioning systems, even the high efficiency Air Source Heat Pumps. At the same time, though, they require considerably higher installation costs. The utilization of dwellings' foundations as ground heat exchanger components has recently demonstrated the potential to generate significant cost reductions primarily attributed to the reduction in expenses associated with drilling and backfill material (grout). These elements are referred to in the literature as Thermo-Active Structures or Energy Geo-structures (EGs). The current study employs a ‘mixed studies’ review (i.e., literature review, critical review and state-of-the-art review) methodology to comprehensively examine and assess the compatibility and integration of different renewable energy sources and environmentally friendly technologies with foundation elements deployed as EGs. These mainly include heat pumps, district heating and cooling networks, solar-thermal systems, waste heat, biomass and other types such as urban structures. Emphasis has been given on the advancement on this area, with the current study identifying and addressing two primary categories. The first category involves the integration of EG elements with sources that are able to supply green electricity, referring to renewable energy electricity obtained from on-grid or off-grid integration. The second category, involves a direct or indirect integration with sources that provide heat, or vice versa. The technical and non-technical barriers of such integrations have been discussed in detail, with the technical challenges generally involving engineering design, and system optimization, whereas non-technical challenges encompassing the economic, social, and policy domains.

Analysis of the ion collection model in the ExB probe

An ExB probe is a pass-band velocity filter for an ion beam. The ExB probe measurement is related to the ion velocity distribution function (IVDF); however, the finite pass-band filter window size leads to differences in the true IVDF and measured ExB probe spectrum. We derive for the first time an analytical ExB probe transmittancy matrix and use it to examine differences in the IVDF and the probe spectrum. The probe spectra are compared to a synthetically defined test IVDF to study how probe geometry and ion species affect the differences. It is found that the difference in the probe spectrum and the true IVDF is dependent on the ion species, and the deviation is larger for heavier ions. The peak velocity of the spectrum was shifted by up to 13%, and the velocity spread was broadened by up to 276%. The relative ion species fraction is calculated from the probe spectra by two different methods and compared to the true fraction. Using the approach of this work, direct integration of the spectrum resulted in a 2% difference, while a more common approach from literature overestimated one ion species by 184%.

OPTIMIZING LEARNING: A META-ANALYSIS OF TIME MANAGEMENT STRATEGIES IN UNIVERSITY EDUCATION

This meta-analysis rigorously investigates time management strategies within university education and their impact on academic performance, student satisfaction, and self-efficacy. Covering two decades (2004-2024), it synthesizes findings from both random and nonrandom controlled intervention studies, providing a comprehensive examination of pedagogical impacts. The analysis reveals nuanced but significant enhancements across academic and personal development dimensions, with varied effect sizes (average g values). Interventions were categorized based on their primary focus—either direct time management skills enhancement or integration within broader academic and personal development strategies. Directly targeting time management proficiency was pivotal in bolstering academic performance and self-efficacy, while broader interventions significantly elevated student satisfaction. This analysis highlights the critical interplay between time management strategies, self-efficacy, and satisfaction, suggesting that tailored, skill-specific interventions can yield substantial benefits in academic contexts. The findings advocate for a holistic approach in higher education pedagogy, emphasizing the necessity of embedding effective time management training within university curricula to optimize learning outcomes and student development. This study contributes to the academic discourse on educational strategies and underscores the imperative for empirical, evidence-based approaches in curriculum design and student support services, guiding future research in educational psychology.

A new pair of block techniques for direct integration of third-order singular IVPs

This paper proposes a new pair of block techniques (NPBT) for the direct solution of third-order singular initial-value problems (IVPs). The proposed method uses a polynomial and two intermediate points to approximate the theoretical solution of third-order singular IVPs, resulting in a reasonable approximation within the integration interval. The method's essential features, including stability and convergence order, are analyzed. The proposed NPBT method is improved by using an embedding-like strategy that allows it to be executed in a variable step size mode in order to gain better efficiency. The effectiveness of the proposed method is assessed using various model problems. The approximate solution provided by the proposed NPBT method is more accurate than that of the existing methods utilized for comparison. This efficient solution positions NPBT as a good numerical method for integrating third-order singular IVP models in the fields of applied sciences and engineering.

A mesh-free framework for high-order simulations of viscoelastic flows in complex geometries

The accurate and stable simulation of viscoelastic flows remains a significant computational challenge, exacerbated for flows in non-trivial and practical geometries. Here we present a new high-order meshless approach with variable resolution for the solution of viscoelastic flows across a range of Weissenberg numbers. Based on the Local Anisotropic Basis Function Method (LABFM) of King et al. (2020), highly accurate viscoelastic flow solutions are found using Oldroyd B and PPT models for a range of two dimensional problems — including Kolmogorov flow, planar Poiseulle flow, and flow in a representative porous media geometry. Convergence rates up to 9th order are shown. Three treatments for the conformation tensor evolution are investigated for use in this new high-order meshless context (direct integration, Cholesky decomposition, and log-conformation), with log-conformation providing consistently stable solutions across test cases, and direct integration yielding better accuracy for simpler unidirectional flows. The final test considers symmetry breaking in the porous media flow at moderate Weissenberg number, as a precursor to a future study of fully 3D high-fidelity simulations of elastic flow instabilities in complex geometries. The results herein demonstrate the potential of a viscoelastic flow solver that is both high-order (for accuracy) and meshless (for straightforward discretisation of non-trivial geometries including variable resolution). In the near-term, extension of this approach to three dimensional solutions promises to yield important insights into a range of viscoelastic flow problems, and especially the fundamental challenge of understanding elastic instabilities in practical settings.

The emotion of sound target modulates the auditory gaze cueing effect

ABSTRACT The auditory gaze cueing effect (auditory-GCE) is a faster response to auditory targets at an eye-gaze cue location than at a non-cue location. Previous research has found that auditory-GCE can be influenced by the integration of both gaze direction and emotion conveyed through facial expressions. However, it is unclear whether the emotional information of auditory targets can be cross-modally integrated with gaze direction to affect auditory-GCE. Here, we set neutral faces with different gaze directions as cues and three emotional sounds (fearful, happy, and neutral) as targets to investigate how the emotion of sound target modulates the auditory-GCE. Moreover, we conducted a controlled experiment using arrow cues. The results show that the emotional content of sound targets influences the auditory-GCE but only for those induced by facial cues. Specifically, fearful sounds elicit a significantly larger auditory-GCE compared to happy and neutral sounds, indicating that the emotional content of auditory targets plays a modulating role in the auditory-GCE. Furthermore, this modulation appears to occur only at a higher level of social meaning, involving the integration of emotional information from a sound with social gaze direction, rather than at a lower level, which involves the integration of direction and auditory emotion.

Investigating the Potential Use of Ni-Mn-Co (NMC) Battery Materials as Electrocatalysts for Electrochemical Water Splitting.

The imminent generation of significant amounts of Li ion battery waste is of concern due to potential detrimental environmental impacts. However, this also poses an opportunity to recycle valuable battery materials for later use. One underexplored area is using commonly employed cathode materials such as nickel, manganese cobalt (NMC) oxide as an electrocatalyst for water splitting reactions. In this work we explore the possibility of using NMC materials of different metallic ratios (NMC 622 and 811) as oxygen evolution and hydrogen evolution catalysts under alkaline conditions. We show that both materials are excellent oxygen evolution reaction (OER) electrocatalysts but perform poorly for the hydrogen evolution reaction. NMC 622 demonstrates the better OER activity with an overpotential of only 280 mV to pass 100 mA cm-2 and a low tafel slope of 42 mV dec-1. The material can also pass high current densities of 150 mA cm-2 for 24 h while also being tolerant to extensive potential cycling indicating suitability for direct integration with renewable energy inputs. This work demonstrates that NMC cathode materials if recovered from Li ion batteries are suitable OER electrocatalysts.

Longitudinal Sentiment Analysis with Conversation Textual Data

AbstractThe inherent qualitative nature of textual data poses significant challenges for direct integration into statistical models. This paper presents a two-stage process for analyzing longitudinal textual data, offering a solution to this inherent challenge. The proposed model comprises (1) initial data preprocessing and sentiment extraction, followed by (2) applying a growth curve model to analyze the extracted sentiments directly. The paper also explores four distinct approaches for extracting sentiment scores in the dialogue, providing versatility to the proposed framework. The practical application of the proposed model is demonstrated through the analysis of an empirical longitudinal textual dataset. This framework offers a valuable contribution to the field by addressing the challenges associated with modeling qualitative textual data, providing a robust methodology for extracting and analyzing sentiments longitudinally.

Artificial intelligence in digital marketing

Development of a comprehensive approach to the integration of artificiale intelligence (AI) into a companyʼs marketing strategy in the digital environment is important to directly ensure the loyalty of customers and achieve an economically primed level of sales conversion period. In this article it was focused on the direct integration of digital marketing algorithms of artificiale inteligence to optimize interaction between companies and target audiences. During the research, the use of fundamental scientific methods of analysis and synthesis was carried out to characterize the AI main algorithms that are used in digital marketing; empirical methods, graphical images, and sys­tem structural analysis. The AI role in digital marke­ting has been emphasized and the impor­tance of using current algorithms to ensure effective communications between com­pa­nies and vendors has been proved. A compr­ehensive analysis of the main digital marketing tools and the features of their use to ensure the competitive position of companies on the Internet was carried out. The scheme of obtain­ning informa­tion from users and optimizing the use of AI tools based on the applying of effective mathematical algorithms is given. The key trends in the development of the market for generative AI in the field of digital marketing have been identi­fied. A subdivision of content created by gene­rative AI has been presented. It has been determined that piece intelligence is a priority in the marketing strategies of companies in the digital environment, which allows companies to ensure personalization of the approach to each client.

In-situ physical/chemical cross-linked hydrogel electrolyte achieving ultra-stable zinc anode-electrolyte interface towards dendrite-free zinc ion battery

Hydrogen evolution reaction (HER), zinc corrosion, and dendrites growth on zinc metal anode are the major issues limiting the practical applications of zinc-ion batteries. Herein, an in-situ physical/chemical cross-linked hydrogel electrolyte (carrageenan/polyacrylamide/ZnSO4, denoted as CPZ) has been developed to stabilize the zinc anode-electrolyte interface, which can eliminate side reactions and prevent dendrites growth. The in-situ CPZ hydrogel electrolyte improves the reversibility of zinc anode due to eliminating side reactions caused by active water molecules. Furthermore, the electrostatic interaction between the SO4−· groups in CPZ and Zn2+ can encourage the preferential deposition of zinc atoms on (002) crystal plane, which achieve dendrite-free and homogeneous zinc deposition. The in-situ hydrogel electrolyte offers a streamlined approach to battery manufacturing by allowing for direct integration into the battery. Subsequently, the Zn//Zn half battery with CPZ hydrogel electrolyte can enable an ultra-long cycle over 5500 h at a current density of 0.5 mA cm−2, and the Zn//Cu half battery reach an average coulombic efficiency of 99.37%. The Zn//V2O5-GO full battery with CPZ hydrogel electrolyte demonstrates 94.5% of capacity retention after 2100 cycles. This study is expected to open new thought for the development of commercial hydrogel electrolytes for low-cost and long-life zinc-ion batteries.

Signal Decomposition for Monitoring Systems of Processes

This article is devoted to the problem of signal decomposition into periodic and aperiodic components. According to the proposed approach, there is no need to evaluate the aperiodic component as a difference between the total signal of its periodic components. This research aims to create a general analytical approach that combines the Fourier and Maclaurin series methodologies into a single comprehensive series. As a result, analytical expressions for determining deposition coefficients were established for an aperiodic signal with a monoharmonic overlay. Recurrence relations were established to determine the coefficients of this series. These relations allow direct integrations of the obtained values of integrals to be avoided. The evaluated numerical values of the coefficients are also presented graphically and tabulated. It was proven that the values of these coefficients are universal numbers since they do not depend on the period/frequency of oscillations. The reliability of the proposed approach was confirmed by the fact that the evaluated coefficients are equal to the Fourier series coefficients in the case of a periodic signal. Also, for an aperiodic signal, these coefficients were reduced to the coefficients of the Maclaurin series. The usability of the proposed generalized analytical approach for signal decomposition is for control and monitoring systems of processes.

Predicting treatment response in multicenter non-small cell lung cancer patients based on federated learning

BackgroundMulticenter non-small cell lung cancer (NSCLC) patient data is information-rich. However, its direct integration becomes exceptionally challenging due to constraints involving different healthcare organizations and regulations. Traditional centralized machine learning methods require centralizing these sensitive medical data for training, posing risks of patient privacy leakage and data security issues. In this context, federated learning (FL) has attracted much attention as a distributed machine learning framework. It effectively addresses this contradiction by preserving data locally, conducting local model training, and aggregating model parameters. This approach enables the utilization of multicenter data with maximum benefit while ensuring privacy safeguards. Based on pre-radiotherapy planning target volume images of NSCLC patients, a multicenter treatment response prediction model is designed by FL for predicting the probability of remission of NSCLC patients. This approach ensures medical data privacy, high prediction accuracy and computing efficiency, offering valuable insights for clinical decision-making.MethodsWe retrospectively collected CT images from 245 NSCLC patients undergoing chemotherapy and radiotherapy (CRT) in four Chinese hospitals. In a simulation environment, we compared the performance of the centralized deep learning (DL) model with that of the FL model using data from two sites. Additionally, due to the unavailability of data from one hospital, we established a real-world FL model using data from three sites. Assessments were conducted using measures such as accuracy, receiver operating characteristic curve, and confusion matrices.ResultsThe model’s prediction performance obtained using FL methods outperforms that of traditional centralized learning methods. In the comparative experiment, the DL model achieves an AUC of 0.718/0.695, while the FL model demonstrates an AUC of 0.725/0.689, with real-world FL model achieving an AUC of 0.698/0.672.ConclusionsWe demonstrate that the performance of a FL predictive model, developed by combining convolutional neural networks (CNNs) with data from multiple medical centers, is comparable to that of a traditional DL model obtained through centralized training. It can efficiently predict CRT treatment response in NSCLC patients while preserving privacy.